Application of Genetic Algorithm to Scheduling of Tour Guides for Tourism and Leisure Industry
Rong-Chang Chen Dept. of Logistics Engineering and Management National Taichung Institute of Technology No.129, Sec 3, San-min Rd., Taichung, Taiwan 404, R.O.C.
[email protected]
Hsiao-Lung Wang Graduate Institute of Sports and Leisure Management National Taiwan Normal University No.162, He-ping East Road, Section 1,Taipei, Taiwan 106, R.O.C.
[email protected]
Abstract
the better the service quality will be. However, more tour guides will cost businesses more money. To provide suitable quantity of tour guides without reducing service quality, many SCc need an effective system to schedule the tour guides. Scheduling tour guides of SCc normally involves dealing with wide ranges of quantities demanded. For example, the quantity of visitors on holidays is likely to be huge, while the quantity on weekdays is likely to be small. The quantities can range from about several hundreds to tens of thousands, making the arrangement of tour guides difficult. Thus, it is not practical to hire a lot of full-time employees to be tour guides since it costs too much money and can not have a high employee utilization rate. To address this kind of problem in a way that can both meet the unstable demands and can save the labor cost, many SCc sign up some part-time tour guides instead of full-time ones. The wages for the part-time guides are usually based on their actual service time. Some SCc do not pay any money to the part-time guides when they are idle during the working hours (from 8 a.m. to 5 p.m. normally), while some pay them a half of their normal hourly wage. The scheduling of tour guides, therefore, has become a very important issue for some SCc. To schedule the tour guides well, many SCc request visitors to reserve in advance of their intended visit date. Hence, schedulers can aggregate demands and arrange the schedules. To facilitate the schedule, schedulers generally divide a big visitor group into some subgroups. A higher number of subgroups may lead to a positively higher rate of tour guide utilization but a negatively higher total guiding time, which implies higher guide cost. In addition, to best meet the requirements of customers’ needs, higher service levels (on-time service
In order to improve service quality, many service centers (SCs) in tourism and leisure industry arrange a lot of activities and provide some tour guides to lead tourists through the tour process. An increase in the number of tour guides generally leads to better service quality. However, more tour guides also result in more cost for SCc. To cut cost, a time-based system which pays wages to employees according to their service hours is commonly adopted in recent years. Consequently, a schedule of tour guides with an objective of minimizing service hours is greatly needed. In this paper, we apply the genetic algorithm (GA) to schedule tour guides of SCc for tourism and leisure industry. Optimal parameters including crossover rates and mutation rates that generate the best performance experimentally are obtained. Experimental results show that GA is effective to schedule the tour guides of SCs. In addition, a penalty function is useful to increase the on-time service rates of visitor orders.
1. Introduction High service quality can be a competitive advantage for many organizations, especially in tourism and leisure industry, to stay ahead of their competitors. With the aim of increasing competitive advantages, organizations design many kinds of interesting activities and establish service centers (SCs) to provide qualified tour guides to guide the visitors. To ensure high service quality, some organizations employ tour guide coordinators to train qualified tour guides and to arrange these guides to serve tourists [1]. Generally, the more tour guides SCc offer, INFOS2008, March 27-29, 2008 Cairo-Egypt © 2008 Faculty of Computers & Information-Cairo University
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rates) are usually required. The on-time service rate which means the percentage of on-time service orders is a very important performance metric for many SCc today. It is very difficult to arrange each order requested by a visitor group within a short period in a manner of fulfilling the company’s objective manually. Thus, an effective scheduling system that can meet different requirements of an organization is needed. In this paper, we investigate the scheduling problem of tour guides and use an effective method to obtain good solutions. Optimal results are experimentally found and some suggestions are presented to better design a scheduling system for SCc. In this study, we use genetic algorithm (GA) [2-7] as the analytical tool of the tour guide scheduling. To our knowledge, there is no paper dealing with tour guide scheduling using GA. On the other hand, quite a few pervious studies confirm that GA is useful in scheduling and it can obtain feasible solutions within short time [3-16]. Thus, we will use GA to solve the problem. The remainder of this paper is structured as follows. The scheduling problem of tour guides of SCc is briefly introduced in Section 2. The approach is addressed in Section 3. In Section 4, the results and discussion are presented. To bring to a close, conclusions are drawn and some suggestions for future investigations are given in Section 5.
2. Tour Guide Scheduling of Service Centers The tourism and leisure industry is considered to be one of the most promising industries in recent years. It continues to rapidly develop and plays a major role in the economic life internationally [17]. Because of higher level of living, leisure and recreation become more and more popular. As a result, improving service levels of SCc has turned out to be a focused issue recently. In the service process of some SCc, one of the most important operations is the tour guide scheduling. Only when an efficient and effective scheduling of tour guides is arranged can an SC keeps up its competitive advantages in modern competing environments. Thus, a good scheduling system is urgently needed for many SCc. However, it is not easy for an SC to find a suitable scheduling system which can arrange tour guides efficiently and effectively for versatile demands in practices. In managing the scheduling problem of tour guides, one of the most important issues is about the service time of tour guides. To save labor cost, many SCc employ part-time tour guides to serve visitors. The wages of
these tour guides are calculated based on the service time. Thus, a schedule of tour guides that provides lower total service time is preferred. To reduce the total service time, the waiting time should be lowered as much as possible. In some situations, an additional time is required if the service sequence of a tour guide is not arranged well. For example, some SCc offer visitors colorful hand-made souvenirs, which require some skilled tour guides to lead visitors to complete the hand-made procedure in which the visitors need to dye the fabrics with dyeing equipment. An additional preparation time to clean the dyeing equipment will require if the dyeing of the fabrics is first a darker color and then followed by a lighter color. The additional setup time can be avoided with a good schedule. It is thus of great importance to find a good method that can reduce the preparation time. A further important issue is the compromise between the service capacity and the service quality. To ensure good quality, a guide should not direct too many visitors at a time. However, directing fewer visitors will cost more because of needing more guides. Generally, a guide is assumed to direct 15-25 visitors per activity. In this paper, we will investigate the influence of service capacity on the scheduling.
3. The Proposed Approach In this section, we first describe the problem and then present the modeling. Finally, the method of solution is presented.
3.1. Problem Description The problem can be described as a single service station with a number of tour guides who direct different visitor groups. The guide time is fixed for a guide to serve a visitor group. A visitor group is normally divided into some subgroups before being served. Each subgroup is assigned to only one tour guide. The tour guides can be categorized into several types. Each type has a fixed service capacity and a fixed preparation time, which is required when the service sequence is in a worse order. The flow for assigning tour guides is shown in Fig. 1. Totally, there are N subgroups (orders) and M tour guides. An additional preparation time will occur when the service sequence number of the former subgroup is higher than the following one for two adjacent subgroups to be served by a certain tour guide, as depicted in Fig. 2. The problem focused in this study is to decrease the preparation time so as to obtain the minimal total service time (actual guiding time plus preparation time).
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The first part Tij in Eq. 1 is the actual guiding time and xij is an indicator variable that takes the value 1 of guide i is assigned to group j and zero otherwise. In the second part, an additional preparation time is considered. The preparation time is the product of the {0,1} variable yi and si, where si is the preparation time of the ith tour guide. This term is due to the improper service sequence of arrangement of visitor subgroups. yi = 1 if the service sequence number of the former subgroup is higher than the following one for two subsequent visitor subgroups served by a certain guide. Otherwise, yi = 0. Different tour guides have different preparation time si. A more skilled tour guide has shorter preparation time.
3.2. Assumptions Fig.1. A schematic diagram of tour guide assignment with N subgroups (orders) and M tour guides.
Fig. 2. Equipment preparation (setup) time: if the service sequence number in the former subgroup is higher than in the latter subgroup, an additional preparation time is required. Let G = {1, 2, ..., M} be a set of tour guides, and let V = {1, 2, ..., N} be a set of visitor subgroups. For i ∈G, j ∈ V, we define Tij as the guiding (service) time by guide i to being assigned subgroup j. The mathematical formulation of this problem can be given by M
minimize F =
N
∑ ∑ {T x ij
i =1 j =1
ij
+ si y i } (1)
subject to
xij ∈ {0,1}
∀i ∈ G, j ∈ V (2)
yi ∈ {0,1}
∀i ∈ G
To solve the problem, the following assumptions are made. (1) The service capacity is fixed for a certain tour guide. (2) The preparation time of a specific tour guide, which results from a poor service sequence of visitor subgroups, is constant. (3) The service sequence can be roughly divided into k categories, where k is a positive integer. Each category is represented by a positive integer, from 1 to k. (4) A visitor group can be divided into some smaller subgroups. Each subgroup is assigned to a tour guide only. (5) The number of tour guides is known. (6) The normal working hours of a day for a guide are 8 hours.
3.3. Input Data Some important data must be given before scheduling. The data include the number of visitors, the service capacity of a tour guide, the stay time of a visitor group, and so on. The number of visitors ranges from several hundreds to tens of thousands. The service capacity depends on the experience of a tour guide. An experienced tour guide is expected to lead more visitors without decreasing service levels than a new tour guide at a time. As for the stay time, tourists can select to stay at the tourism and leisure center half day or one day. An original customer order includes the following data: visitor group index number, visitor group name, number of visitors, and the stay time. To facilitate the scheduling, the original customer order is generally divided into some smaller orders with fewer visitors. Some main information of the inputted data to the program is shown in Table 1.
(3)
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Table 1. Important input data concerning the visitor. Description Quantity
The quantity of visitors
Value A positive integer
The service can be divided into several categories. An additional preparation time will occur when the service sequence number of the 1, 2, 3, …, k former subgroup is higher than the following one for two adjacent subgroups for a certain tour guide Half day, one day 4, 8 hrs
Service sequence number
Stay time
To schedule the tour guides for SCs, the data of service capacity of tour guides are also needed. For an experienced tour guide, the service capacity can be as high as 25, while for a new one, the service capacity is 15. Table 2 illustrates the necessary data for scheduling. The other important input datum is the preparation time, which also depends on the tour guide. In general, an experienced tour guide requires less time to prepare. Table 2. Input data concerning tour guides Description Service capacity High, fair, low Depending on the tour guide. An experienced Preparation time tour guide requires less time to prepare.
After completing the encoding of chromosome, we need a fitness function to measure the performance. The fitness function measures the fitness of the minimum total guiding time. A schedule which has the minimum total guiding time stands for the best schedule. The lower the total guiding time, the better is the assignment of subgroups to tour guides. The fitness function is composed of three parts, as shown in Eq. 4. M
F=
i =1 j =1
ij ij
+ si yi + Pj z j } (4)
The first part is the actual guiding time. In the second part, an additional preparation time is considered. The final term in Eq. 4 is the product of {0,1} variable zj and the penalty function Pj, which is related to the relative importance of the visitor subgroups. The penalty function value for a more important subgroup is higher than other subgroups. The final term can be used to increase the on-time service rates.
3.5. Solution Procedure
25, 20, 15 1 – 2 hrs
The procedure for GA is depicted in Fig. 4. The encoding method in this paper is the numerated encoding, in which the gene is represented by an integer number. After encoding, we need to generate an initial population, which stands for a group of possible solutions. We adopt the random method, which explores a wider solution space, to generate the initial population. Better solutions are retained according to the fitness function value F.
The encoding of chromosome is illustrated in Fig. 3. C represents the chromosome in the population. In a chromosome, each gene provides two pieces of information: (i) the gene sequence number represents the subgroup index number; and (ii) the value in the gene indicates the index number of a tour guide. A subgroup is assigned to only one guide. For example, the value of the first gene is 5, indicating the first subgroup is assigned to the tour guide with an index number of 5. The value of the second gene is 1 and this means the second subgroup is assigned to the guide with an index number of 1.
Encode Initialize the population
Evaluate the fitness function Y
Output and
Terminal condition Decode N select Crossover
Subgroup index number
Mutate
1
2
3 4
5
6 7
5
1
2
7
6
4
∑∑ {T x
Value
3.4. Encoding and Fitness Function
C
N
Go to the new generation
3
Fig. 4. The procedure for getting solutions. Gene (Tour guide index number)
Fig. 3. Encoding of chromosome.
The termination condition used in this paper is when the evolution reaches a given generation number. To
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investigate the influence of the generation number on the solution, different generation numbers are set and the solutions are compared. In the crossover process, we used the two-point crossover method to generate offspring. Initially, two points are randomly chosen. Thus, there are three fragments in each chromosome. The offspring is then created by copying the first fragment from chromosome 1, the second fragment from chromosome 2, and the third fragment from chromosome 1 again. Since the number for each gene does not require being unique, the procedure is quite straightforward and easy. As illustrated in the following figure, 1, 5, 4, 3, and 6 are copied from chromosome 1. Therefore, they are removed from chromosome 2. The remained numbers are 8, 7 and 2. Thus, 8, 7, and 2 are copied to generate the offspring.
4. Results and Discussion In this paper, we employed GA to solve the tour guide scheduling problem. We used Microsoft Visual C++ to develop the program. The operating system was Window 2000. The crossover and the mutation methods which were used to find a solution in this paper were two-point crossover and two-point swapping mutation, respectively. To investigate the influences of genetic parameters on the performance, we let the quantity of visitors to be 3,200 and consider it as the base case. For brevity of description, we designate the generation number as g, the crossover rate as Pc, the mutation rate as Pm, the population size as P, the number of tour guides as M, the number of visitor subgroup as N, the average best fitness value Fbest as AVG, the minimum best fitness value MIN, and the standard deviation of best fitness value Fbest as STD, where Fbest is the best fitness value calculated from Eq. 4 over g generations. In addition, the service capacity is designated by Ca, the on-time service rate by Ron-time, and guide utilization rate by Rutilization.
4.1. Optimal Parameters
Fig. 5. Crossover is done by two-point crossover method. The mutation method we used is the swap method, as indicated in the Fig. 6.
To find optimal parameters, first the influence of variation of the generation number g with the fitness value was tested. The optimal generation number was chosen based on the best fitness value Fbest. The generation number, g, was varied from 50 to 600 and 500 was found to be a good parameter value since it gives a lower AVG with a smaller STD, as shown in Fig. 7. The point indicates AVG and the length between the bar and the point equals to STD. All the results are based on 30 times calculations. AVG 230 220 210 200 Fbest
190 180 170 160 150 0
Fig. 6. Mutation is done by an exchange of two points.
100
300 400 500 200 Generation Number, g
600
Fig. 7. The influence of variation of generation number g on the Fbest.
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The population size was set to be 50, 100, 200, 300 and 500 and the results showed that 300 is a suitable parameter value because it gives a good solution and reasonable execution time. Thus, the following experiments were run with a population size P = 300 and a generation number g = 500. MIN
AVG
Table 4. The influence of variation of mutation rate on the Fbest. (All the results are based on 30 times calculations)
STD
25 20 Fbest
Pm
MIN
AVG
STD
0.01
170
176.54
3.78
0.02
168
173.57
2.49
0.05
168
170.87
1.48
0.1
165
168.73
1.31
0.2
164
167.77
1.55
4.2. Effects of Penalty Function
15
The on-time service rate (or the non-delayed rate) Ron-time is defined as:
10 5
Ron−time =
0 0
100
200
300
No. of on - time service orders No. of total visitor orders
(5)
40
Population Size, P
Fig. 8. The influence of variation of population size P on the best fitness value Fbest.
Ron-time can be increased by employing the penalty function Pj, as shown in Eq. 4. When the value of the penalty function is increased, the Ron-time is also increased. Table 5 shows this trend.
As for the crossover rate Pc, the experiments showed that Pc = 0.9 is better than other values. The variation of best fitness value with the crossover rate is shown in the Table 3.
Table 5. The influence of penalty value Pj on the performance of scheduling.
Table 3. The influence of variation of crossover rate on the Fbest. (All the results are based on 30 times calculations) AVG
Pj
si
Total delay time
Ron-time (%)
1
0.80
7.93
95.2
5
2.83
5.23
96.7
Pc
MIN
AVG
STD
10
2.93
4.97
96.9
0.5
168
173.80
2.73
20
3.10
5.27
96.7
0.6
167
172.30
2.70
1
0.89
1.41
0.80
0.7
168
172.50
2.35
5
0.83
0.86
0.54
0.8
165
171.67
2.76
10
0.78
1.07
0.67
0.9
168
170.87
1.48
20
0.88
1.17
0.73
STD
In a similar way, the best mutation rate Pm can be obtained. The experiments showed that Pm = 0.1 is the best parameter value. The variation of best fitness value with the crossover rate is shown in the Table 4.
4.3. Effects of Service Capacity The effects of service capacity are illustrated in Table 6. For comparison, the number of visitors is fixed as 3,000. If the number of guides M is fixed, an increase in the service capacity will increase Ron-time. However, the Rutilization will first increase and then decrease, indicating that there is a maximum utilization. On the other hand, if M × Ca is kept constant, a higher value of Ca will lead to a higher value of Ron-time and a higher value of Rutilization. Note that, however, a higher value of Ca will generally
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reduce the service quality if the tour guides are not well trained. Table 6. Effects of service capacity on the average on-time service rate and guide utilization rate
research was supported in part by the National Science Council through Grant NSC 95-2221-E-025-011.
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M
Ca
Average Ron-time (%)
12
25
67.8
92.4
15
20
66.8
91.9
[4]
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66.7
91.6
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85.7
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5. Conclusions
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In dealing with the tour guide scheduling in service centers (SCc), many businesses need to respond to unstable demands. High responsiveness to unstable demands can be a competitive advantage for a firm in highly competing industries. To stay ahead of competitors, SCc should be able to schedule tour guides in an efficient way. The purpose of this paper is to investigate the scheduling problem of tour guides in SCc. Genetic algorithm (GA) is employed to be the analytical tool. Results from this paper show that by using GA, the scheduling problem can be well solved within short time. To schedule tour guides with lower total guiding time, one can divide a big visitor group into some subgroups with smaller quantities. As the number of divided subgroups increase, the tour guide utilization is increased but the average total guiding time and the coefficient of variation are also increased. To obtain higher on-time service rates for short due dates, an additional penalty factor can be added. Experiments show that the on-time service rate can be increased by a higher penalty value. Moreover, optimal parameters including mutation rates and crossover rates that generate good performance are obtained. Future works are encouraged to address the fulfillment of multiple objectives for SCc. In addition, some visitors prefer assigning an interval of stay time instead of staying a half day or all day. A further study may develop a system that can meet this requirement.
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Acknowledgment The authors wish to express their sincere appreciation to the anonymous reviewers for their valuable comments and suggestions which helped improve the paper. This
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